Causal Fermion Systems: Discrete Space-Times, Causation and Finite Propagation Speed

Abstract: The theory of causal fermion systems is a recent approach to fundamental physics. Giving quantum mechanics, general relativity and quantum field theory as limiting cases, it is a candidate for a unified physical theory. The dynamics is described by a novel variational principle, the so-called causal action principle. The causal action principle does not rely on a presupposed space-time structure. Instead, it is a variational principle for space-time itself as well as for all structures in space-time (like particles, fields, etc.). After a general motivation and introduction, we report on mathematical results for two-particle causal fermion systems which state that every minimizer describes a discrete space-time. We explain and make precise that on scales which are much larger than the scale of the microscopic space-time structures, the dynamics of a causal fermion system respects causality with a finite speed of propagation.